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Prove that vectors vecu=(al+a(1)l(1))h...

Prove that vectors
`vecu=(al+a_(1)l_(1))hati+(am+a_(1)m_(1))hatj + (an+a_(1)n_(1))hatk`
`vecv=(bl+b_(1)l_(1))hati+(bm + b_(1)m_(1))hatj+(bn+b_(1)n_(1))hatk`
`vecw=(wl+c_(1)l_(1))hati+(cm+c_(1)m_(1))hatj+(cn+c_(1)n_(1))hatk`

A

form an equilteral triangle

B

are coplanar

C

are collinear

D

are mutually perpendicular

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B
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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. (vecbxxvecc)xx(veccxxveca)=

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  2. When a right handed rectangular Cartesian system OXYZ is rotated about...

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  3. Prove that vectors vecu=(al+a(1)l(1))hati+(am+a(1)m(1))hatj + (an+a(...

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  4. If vecaxx(vecaxxvecb)=vecbxx(vecbxxvecc) and veca.vecb!=0, then [(veca...

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  5. [(veca,vecb,axxvecb)]+(veca.vecb)^(2)=

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  6. Let vec(alpha),vec(beta) and vec(gamma be the unit vectors such that v...

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  7. If veca, vecb and vecc are unit coplanar vectors, then [(2veca-3vecb,...

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  8. If [(veca,vecb,vecc)]=3, then the volume (in cubic units) of the paral...

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  9. If V is the volume of the parallelepiped having three coterminous edge...

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  10. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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  11. If vectors vec A B=-3 hat i+4 hat ka n d vec A C=5 hat i-2 hat j+4 ha...

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  12. Let the position vectors of vertices A,B,C of DeltaABC be respectively...

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  13. The position vector of a point P is vecr=xhati+yhatj+zhatk where x,y,z...

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  14. veca and vecb are two unit vectors that are mutually perpendicular. A...

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  15. If the vectors 2ahati+bhatj+chatk, bhati+chatj+2ahatk and chati+2ahatj...

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  16. Let alpha = a hati + b hatj + chatk , vecbeta = bhati + chatj + ahatk ...

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  17. Let veca,vecb,vecc be three mutually perpendicular vectors having same...

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  18. Let veca,vecb and vecc be the three non-coplanar vectors and vecd be a...

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  19. Let vecr be a unit vector satisfying vecr xx veca = vecb, " where " |v...

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  20. Let veca and vecc be unit vectors such that |vecb|=4 and vecaxxvecb=2(...

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